The answer to the logarithmic equation

x = -8 and x = 2

To find this, follow these steps:

Since it's addition with the same log base, you need to multiply the two together:

x multiplied with x + 6 which produces x^2 + 6x

This then leaves you with:

logbase 4 (x^2 + 6x) = 2

To get rid of the log base, you need to use the base given (4) and set it to the power of 2 due to the fact that that is what is on the opposing side.

X^2 + 6x = 4^2

x^2 + 6x = 16

Now make this into a quadratic and solve for the roots:

x^2 + 6x - 16

(x + 8) (x - 2)

x = -8 and x = 2

Hope this helps!